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ICE Princess25 [194]
2 years ago
12

Find the derivative of the following function, with a positive index (differentiation)

Mathematics
1 answer:
Yakvenalex [24]2 years ago
6 0

Answer:

2nd option

Step-by-step explanation:

Using the power rule

\frac{d}{dx} (ax^{n} ) = nax^{n-1}

Given

f(x) = \frac{3}{2\sqrt[3]{x} } = \frac{3}{2x^{\frac{1}{3} } } = \frac{3}{2} x^{-\frac{1}{3} } , then

f'(x) = - \frac{1}{3} × \frac{3}{2} x^{-\frac{4}{3} }

      = - \frac{1}{2} × \frac{1}{x^{\frac{4}{3} } }

      = - \frac{1}{2x^{\frac{4}{3} } } = - \frac{1}{2\sqrt[3]{x^4} } [ Note there should be a leading negative ]

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